Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation

Author:

El Bahi Maria Ihsane1ORCID,Hilal Khalid1ORCID

Affiliation:

1. Sultan Moulay Slimane University, Bp 523, Beni Mellal 23000, Morocco

Abstract

In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative. With the help of the obtained Lie point symmetries, the equation is reduced to nonlinear fractional ordinary differential equations (NLFODEs) which contain the Erdélyi–Kober fractional differential operator. The equation is also studied by applying the power series method, which enables us to obtain extra solutions. The obtained power series solution is further examined for convergence. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

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